One Sheet Calculus Review
by
Robert G. Brown
Duke University Physics Department
Durham, NC 277080305
Copyright Robert G. Brown, 2015
Abstract
One Sheet Calculus Review
by Robert G. Brown (rgb)
Many students taking introductory physics, especially the first semester
mechanics course, find themselves unable to remember the required
calculus that is a prerequisite for the course. The calculus isn't
particularly difficult  it is just that one only needs a small part of
what was covered in a very long course and often students are several
years out of calculus by the time they take physics.
The One Sheet Calculus Review provided here is a very
terse summary of pretty much all of the calculus you are likely to need
in introductory mechanics. It does not cover the multivariate line and
surface and volume integral concepts needed in introductory electricity
and magnetism, but in fact it is sufficient to do almost all of the
integrals and derivatives required in that course, once one learns how
to break these integrals down into managable (multiple onedimensional)
form. The sheet also contains statements of the Taylor Series and the
Binomial Expansion, both of which are both conceptually and
algebraically invaluable in understanding physics involving "small
perturbations", linear models near equilibrium, and asymptotic forms,
especially in electricity and magnetism but also in mechanics.
Note well that this sheet doesn't provide much by way of examples or
practice at doing the integrals using e.g. usubstitution or applying
the chain rule or integration by parts, but those are skills the
student should have at one time learned, and with just a bit of help and
practice they (or you, if you are downloading this for yourself) can
recover them. Even so, the actual integrals one needs for almost all
of the two semester course are either on this page or easily derived
from what is on this page.
Good luck! Feel free to contact me with e.g. bug reports or
problems.

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